急! Properties of Circles 12q4

13) DE = AD = 2 (Tangent prop)

CE = CB = 8 (Tangent prop)

Hence AB = 28 - 2 x 2 - 2 x 8 = 8

Thus radius of the circle = 4 cm

14) With PR = 10, radius of circle with centre P is 2 cm, hence PQ = 2 cm

Drop a perp. from P to RS and let the foot be T, then PTSQ is a rectangle

PT = √(RP2 - RT2) = √(102 - 62) = 8

Hence QS = 8 cm

15a) BZ = BX (Tangent prop)

Hence △BXZ is an isos. △ with ∠BXZ = ∠BZX = (180 - 52)/2 = 64

Hence ∠YXC = 180 - 64 - 44 = 72

Similarly, △CXY is an isos. △ with ∠CXY = ∠CYX = 72

Hence ∠ACB = 180 - 72 - 72 = 36

b) ∠XYZ = ∠BXZ = 64 (∠ in alt. segment)